1,011 research outputs found
Symmetry and History Quantum Theory: An analogue of Wigner's Theorem
The basic ingredients of the `consistent histories' approach to quantum
theory are a space \UP of `history propositions' and a space \D of
`decoherence functionals'. In this article we consider such history quantum
theories in the case where \UP is given by the set of projectors \P(\V) on
some Hilbert space \V. We define the notion of a `physical symmetry of a
history quantum theory' (PSHQT) and specify such objects exhaustively with the
aid of an analogue of Wigner's theorem. In order to prove this theorem we
investigate the structure of \D, define the notion of an `elementary
decoherence functional' and show that each decoherence functional can be
expanded as a certain combination of these functionals. We call two history
quantum theories that are related by a PSHQT `physically equivalent' and show
explicitly, in the case of history quantum mechanics, how this notion is
compatible with one that has appeared previously.Comment: To appear in Jour.Math.Phys.; 25 pages; Latex-documen
Exact results for one dimensional stochastic cellular automata for different types of updates
We study two common types of time-noncontinuous updates for one dimensional
stochastic cellular automata with arbitrary nearest neighbor interactions and
arbitrary open boundary conditions. We first construct the stationary states
using the matrix product formalism. This construction then allows to prove a
general connection between the stationary states which are produced by the two
different types of updates. Using this connection, we derive explicit relations
between the densities and correlation functions for these different stationary
states.Comment: 7 pages, Late
Random walk theory of jamming in a cellular automaton model for traffic flow
The jamming behavior of a single lane traffic model based on a cellular
automaton approach is studied. Our investigations concentrate on the so-called
VDR model which is a simple generalization of the well-known
Nagel-Schreckenberg model. In the VDR model one finds a separation between a
free flow phase and jammed vehicles. This phase separation allows to use random
walk like arguments to predict the resolving probabilities and lifetimes of jam
clusters or disturbances. These predictions are in good agreement with the
results of computer simulations and even become exact for a special case of the
model. Our findings allow a deeper insight into the dynamics of wide jams
occuring in the model.Comment: 16 pages, 7 figure
- …